The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
Modern Information Retrieval
Maintaining Stream Statistics over Sliding Windows
SIAM Journal on Computing
Improved Algorithms and Analysis for Secretary Problems and Generalizations
SIAM Journal on Discrete Mathematics
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating Rarity and Similarity over Data Stream Windows
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Maintaining variance and k-medians over data stream windows
Proceedings of the twenty-second ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Identifying frequent items in sliding windows over on-line packet streams
Proceedings of the 3rd ACM SIGCOMM conference on Internet measurement
Finding (Recently) Frequent Items in Distributed Data Streams
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Approximate counts and quantiles over sliding windows
PODS '04 Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
What's hot and what's not: tracking most frequent items dynamically
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2003
A multiple-choice secretary algorithm with applications to online auctions
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Approximate quantiles and the order of the stream
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A simpler and more efficient deterministic scheme for finding frequent items over sliding windows
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Smooth Histograms for Sliding Windows
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The hiring problem and Lake Wobegon strategies
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Geometric optimization problems over sliding windows
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Survey: Streaming techniques and data aggregation in networks of tiny artefacts
Computer Science Review
Competitive analysis of maintaining frequent items of a stream
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
The frequent items problem in online streaming under various performance measures
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We consider the problem of maintaining a fixed number k of items observed over a data stream, so as to optimize the maximum value over a fixed number n of recent observations. Unlike previous approaches, we use the competitive analysis framework and compare the performance of the online streaming algorithm against an optimal adversary that knows the entire sequence in advance. We consider the problem of maximizing the aggregate max , i.e., the sum of the values of the largest items in the algorithm's memory over the entire sequence. For this problem, we prove an asymptotically tight competitive ratio, achieved by a simple heuristic, called partition-greedy, that performs stream updates efficiently and has almost optimal performance. In contrast, we prove that the problem of maximizing, for every time t , the value maintained by the online algorithm in memory, is considerably harder: in particular, we show a tight competitive ratio that depends on the maximum value of the stream. We further prove negative results for the closely related problem of maintaining the aggregate minimum and for the generalized version of the aggregate max problem in which every item comes with an individual window.